\documentclass{article}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{plot coordinates/math parser=false}
\usepackage{setspace,subfigure}
\usepackage{tikz}
\usetikzlibrary{plotmarks}
\usetikzlibrary{lindenmayersystems}
\usetikzlibrary{decorations.pathmorphing}
\usepackage{geometry}
\geometry{verbose=false,papersize={2.8in,2.5in},body={2.8in,2.5in},marginratio={4:3, 2:3}}% marginratio={horizontal ratio,verticalratio}
\begin{document}
\thispagestyle{empty}
\null\vspace{0pt}
\hspace{-10pt}
\begin{tikzpicture}
\draw [ green, ultra thick,domain=0:2*pi,samples=100] plot ({1.5*cos(\x r) + (0.3/2)*cos((5+1)*\x r)+(0.3/2)*cos((5-1)*\x r)},{sin(\x r) + (0.3/2)*sin((5+1)*\x r) - (0.3/2)*sin((5-1)*\x r)});



\draw [ purple,ultra thick,domain=0:2*pi,samples=100] plot ({2.7+1.5*cos(\x r) + (0.3/2)*cos((5+1)*\x r)+(0.3/2)*cos((5-1)*\x r)},{1.5+sin(\x r) + (0.3/2)*sin((5+1)*\x r) - (0.3/2)*sin((5-1)*\x r)});
\draw [ purple,ultra thick,domain=0:2*pi,samples=100] plot ({2.7+1.5*cos(\x r) + (0.3/2)*cos((5+1)*\x r)+(0.3/2)*cos((5-1)*\x r)},{-1.5+sin(\x r) + (0.3/2)*sin((5+1)*\x r) - (0.3/2)*sin((5-1)*\x r)});

%bounding contour
%\draw [ green, ultra thick,domain=0:2*pi,samples=100] plot ({1.2*(1.5*cos(\x r) + (0.3/2)*cos((5+1)*\x r)+(0.3/2)*cos((5-1)*\x r))},{1.2*(sin(\x r) + (0.3/2)*sin((5+1)*\x r) - (0.3/2)*sin((5-1)*\x r))});
%bounding contour
\draw[green, ultra thick] (-2,-1.7) -- (-2,1.7) -- (2.3,1.7) -- (2.3,-1.7) -- cycle;
\draw [ green, ultra thick,domain=3*pi/4+0.55:3*pi/4+2,samples=100] plot ({2.7+1.5*cos(\x r) + (0.3/2)*cos((5+1)*\x r)+(0.3/2)*cos((5-1)*\x r)},{1.5+sin(\x r) + (0.3/2)*sin((5+1)*\x r) - (0.3/2)*sin((5-1)*\x r)});
\draw [ green,ultra thick,domain=pi/2+0.35:pi/2+1.8,samples=100] plot ({2.7+1.5*cos(\x r) + (0.3/2)*cos((5+1)*\x r)+(0.3/2)*cos((5-1)*\x r)},{-1.5+sin(\x r) + (0.3/2)*sin((5+1)*\x r) - (0.3/2)*sin((5-1)*\x r)});

%\node [green] at (-0.4,-1.1) {$\Gamma$};
\end{tikzpicture}
\end{document}
